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Smoothed particle hydrodynamics

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Since its introduction in the late 1970s by Lucy [11] and Gingold and Monaghan [4], smoothed particle hydrodynamics (SPH) has been used in many areas. It has grown into a widely-recognized technique with many practical applications. In this thesis, we present a new application of the SPH method: a new algorithm for computing a null divergence velocity field using SPH for incompressible flow - a pure SPH solution of the Helmholtz-Hodge decomposition. Also, a new version of the Laplacian for SPH is proposed and the advantages and disadvantages of different gradient and Laplacian approximation formulas used in SPH are also discussed. A new treatment of boundary conditions is proposed for the whole solution procedure. Throughout the thesis, a brief historical overview is presented, along with some fundamental notions about SPH and computational fluid dynamics.